What is the Expected Wheel Tax Revenue for the City in November?

In summary, the city can expect to receive $3,872,150 in wheel tax revenue in November, assuming a uniform distribution of birthdays. This is calculated by multiplying the number of registered automobiles (74,806) by the annual tax amount ($50) and then multiplying by the probability of having a birthday in November (30/365). For an average year, the expected revenue in February would be $3,170,548.22, calculated by using the same formula and adjusting the probability to account for the varying number of days in February (28/365 for a non-leap year and 29/366 for a leap year).
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1. A city has 74,806 registered automobiles. Each is required to display a bumper decal showing that the owner paid an annual wheel tax of $50. By law, new decals needed to be purchased during the month of the owner’s birthday. How much wheel tax revenue can the city expect to receive in November?



2. expected value = E(X) = summation(x*f(x))
Leibnitz's rule



3. I thought there was not enough information in the problem. Can we assume that people are equally likely to be born in the different months of the year?
Anyway, all I have is E(X) = (74,506*50)*1/12
where the part in parenthesis is x and 1/12 is the probability function
(not sure).
 
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  • #2
I think you are right that you need to assume a uniform distribution of birthdays, and I would write that assumption out explicitly.

Just one question about your answer - what is the expected revenue in (say) February?
 
  • #3
Going by the same approach, it would be the same answer. Did you have something else in mind?
 
  • #4
I think each day is equally likely...
 
  • #5
Ah, I see. So for November, E(X) = (74,506*50)*30/365
and for February, assuming it's not a leap year, it would be E(X) = (74,506*50)*28/365

Thanks for the help.
 
  • #6
That is the right answer for a non-leap year - can you figure it out for an average year?
 

What is an expected value problem?

An expected value problem is a statistical concept that helps determine the average outcome or payoff of a certain event or situation. It takes into account all possible outcomes and their probabilities to calculate the expected value.

How do you calculate expected value?

The expected value is calculated by multiplying each possible outcome by its probability and then summing these values together. For example, if there are three possible outcomes with probabilities of 0.2, 0.3, and 0.5 and the corresponding values are $10, $20, and $30, the expected value would be: (0.2 * $10) + (0.3 * $20) + (0.5 * $30) = $23.

What is the significance of expected value?

Expected value is used in decision-making and risk analysis to help determine the most favorable course of action. It helps to quantify the potential risks and benefits associated with different choices, allowing individuals or organizations to make informed decisions.

What are some common applications of expected value?

Expected value is used in various fields, including finance, economics, and game theory. It can be applied to determine the expected return on investments, evaluate insurance policies, and make strategic decisions in business or politics.

How can I improve my understanding of expected value problems?

To improve your understanding of expected value problems, it is important to practice solving different types of problems and familiarize yourself with the concepts of probability and expected value. Additionally, seeking guidance from a tutor or participating in study groups can also help improve your understanding and skills in this area.

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